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If m is an integer, is m odd?
1) m/2 is not an even integer
2) m – 3 is not an even integer
  • a)
    Exactly one of the statements can answer the question
  • b)
    Both statements are required to answer the question
  • c)
    Each statement can answer the question individually
  • d)
    More information is required as the information provided is insufficient to answer the question
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If m is an integer, is m odd?1) m/2 is not an even integer2) m –...
The second statement is incomplete and does not provide any information about the parity of m.

Statement 1: If m/2 is not an even integer, then m must be an odd integer. This statement alone is sufficient to answer the question, as it confirms that m is indeed odd.

Statement 2: This statement is incomplete and cannot be used to determine the parity of m.

Therefore, the answer is A) Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
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Community Answer
If m is an integer, is m odd?1) m/2 is not an even integer2) m –...
  • Statement 1: “m/2 is not an even integer.”
    • If m is odd, m/2 isn’t an integer (so certainly not an even integer).
    • If m ≡ 2 (mod 4), then m/2 is an odd integer (so again not even).
    • Only if m ≡ 0 (mod 4) would m/2 be even.
    • ⇒ Statement 1 holds for both odd m and for m ≡ 2 (mod 4). You cannot tell if m is odd. Not sufficient.
  • Statement 2: “m – 3 is not an even integer.”
    • If m is odd, m – 3 is even (so that would contradict the statement).
    • If m is even, m – 3 is odd (so not an even integer).
    • ⇒ The statement can only be true if m is even, so you conclude m is not odd. Sufficient.
Answer: A: Exactly one of the statements can answer the question.
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